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Theorem equtr 1873
Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtr  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)

Proof of Theorem equtr
StepHypRef Expression
1 ax7 1868 . 2  |-  ( y  =  x  ->  (
y  =  z  ->  x  =  z )
)
21equcoms 1872 1  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672
This theorem is referenced by:  equtrr  1874  equequ1  1875  equviniv  1880  equvin  1881  ax6e  2107  equvini  2195  sbequi  2224  axsep  4517  bj-axsep  31474
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